Not at all sure what that means.

Sorry, it's the duty cycle in analogWrite()

Did you use a transistor when you drove it with PWM?

I used a MOSFET trigger switch (see annex picture)

PWM connects to your PWM pin on the arduino, ground to the arduino ground.

V-Out + goes to + on the strip and V-Out - goes to blue AND red on the strip.

Normally these sort of strips are run from 12V.

I'm pretty sure that this strip runs on 5V since the power supply provides 5V.

No that is neither Kirchhoff's nor a version of ohms law which is what you should be using.

Well Kirchhoff's second law states that "the algebraic sum of all the voltages around any closed loop in a circuit is equal to zero"

So the power supply provides 5V, the strip has the LEDs parallel to each other, so you could define one LED with resistor (430 Ohms) as one closed loop.

So the voltage over the LED is calculated by subtracting the product of resistance of the resistor (430 Ohms) and the current over the LED (and thus the resistor since they are in line) from the voltage fro the power supply.

5V- (430 Ohms* 10 milliamperes) = 0,7V